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## KEYSTONE SHOWDOWN

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**Question 1**A gallon of paint covers 350-400 square feet, and Chelsea is planning to paint a room with 1440 square feet of wall space. How many gallon cans of paint should Chelsea buy?**Question 2**Billy is 6 years younger than Amy. The sum of their ages is 22. How old will each of them be in 8 years?**Question 3**In which quadrants of the coordinate plane is the shaded region of the system located? y ≥ x y ≤ x + 4 A)I, II and III B)I, II, and IV C)I, III, and IV D)II, III, and IV**Question 4**Michael is trying to determine which gym to join. If Michael chooses LA Fitness, in how many months will his total cost for LA Fitness be less than his total cost for Planet Fitness?**Question 5**Alan, Bill and Charlie are brothers. Bill is x years old. Alan is 1 year younger and Charlie is 1 year older. Write an expression that correctly shows the product of the boys ages.**Question 6**Jim has ten more dollars than Gail. Together they have at most twenty-seven dollars. Write an inequality that shows the possible amounts of money Gail could have.**Question 7**The lockers at Smith High School are numbered 1-1000. Seth starts at the beginning and opens the even numbered lockers. Mike then starts at the beginning and opens all numbers that are multiples of 3. Lastly, Brady starts at the beginning and opens all numbers that are multiples of 5. Which is the first locker that Brady is supposed to open that is already open?**Question 9**A bag of candy contains 3 blue, 5 red, 4 green, and 3 brown pieces. a. What is the probability of picking a blue and then a green, with replacement? b. What is the probability of picking a blue and then a green, without replacement?**Question 10**If f (x) = 2x3 - 4x2 + 2, and g(x) = x3 - 2x2 - 2x + 4,Find f(x) - g(x) =**Question 11**Solve the inequality. (Answer in Interval Notation) |4x - 1| ≥ 23**Question 12**Jasmine notices that the tires on her parents' truck are about 2 feet in diameter. About how many times would the tires revolve during a 10 mile car trip? [1 mile = 5280 feet]]**Question 13**Which of the graphs is the best example of a line of best fit?**Question 14**A concession stand sells hamburgers (h) for $2 and hotdogs (d) for $1. On Friday night they sold a total of 300 hamburgers and hotdogs and made $420. How many of each did they sell?**Question 15**Multiply (3x - 2)2**Question 16**The graph shows the distance Heather is FROM her campsite. About how many miles has she hiked after 2.5 hours?**Question 18**Seats in an auditorium are numbered 1-500, and the principal is handing out snacks in an assembly. Every student whose seat is a multiple of 4 gets chocolate. Every student in a seat that is a multiple of 7 gets jelly beans, and every student in a seat that is a multiple of 10 gets chips. The student in which seat number is the first to get all 3 treats?**Question 19**Mike is saving money earned from a job. For every $20 Mike earns, he puts $4 into savings. Mike is going to graph his savings. The x-axis will be the amount saved, and the y-axis will be the money earned. What will be the slope of Mike's graphed line? Money Earned - $ Hint: it might help to graph the line. Amount Saved - $**Question 20**a. Is there a correlation between how many miles Anna runs and which week it is? If there is, what type? b. Is the slope constant through the entire graph? How do you know? c. What is a good estimation of the slope? d. If the points on the whole numbers represent how many miles she ran at the beginning of each week, what do you think that the points in between the whole numbers represent? e. How many miles did Anna run at the beginning of week 4? f. If the pattern continues, how many miles would you expect her to run at the beginning of week 8? weeks miles**Question 21**Factor the following: x2 + 16**Question 22**The graph shows the distance a car travels at a constant speed. What is the speed of the car?**Question 23**What is the first operation used in solving this equation? 2x + 5 = 10**Question 24**Your teacher has asked you to analyze this set of scores. Show your work for each step. 78 89 85 67 90 75 89 62 88 55 a) Find the mean, median, and mode. b) Suppose you are told that the last score, 55, was actually a 22. Recalculate the mean, median, and mode.**Question 25**The rental costs for a car are shown in the graph. Estimate the rental cost for 6 days.**Question 26**Which of these statements is true about this graph? A)As the independent variable decreases, the dependent variable decreases. B)As the independent variable decreases, the dependent variable increases. C)As the independent variable increases, the dependent variable decreases. D)As the independent variable increases, the dependent variable remains constant.**Question 27**A telephone company offers two plans with per-minute charges. Plan A involves a monthly rental fee of $12, And call charges at 7¢ per minute. Plan B involves a monthly rental fee of $15, and call charges at 5¢ per minute. How many minutes must you use in order for Plan A to cost less than Plan B?**Question 28**The area of the bottom of a shoebox can be written as A(x) = 2x2 - 4 and the height of the shoebox can be written as h(x) = 3x + 2. Write an expression to represent the volume V(x) of the shoebox.**Question 29**• A city had a population of 67,255 on • January 1, 2000, and its population • has been increasing by 2935 • people each year since then. • Write a linear model for the • population P, where t is the time in • years after 2000**Question 30**A garden has a width that is 25 feet less than twice the length, and a length that is 10 feet less than twice the width. Ella wants to put fencing around the garden, which costs $11 per foot. How much will she spend on fencing?**Question 31**Simplify the expression: 5(x + 2)2 - (4x + 3)**Question 32**Eliot found the least common multiple (LCM) of 9a3b2c and 12ab3c2 to be 36a3b2c2. Identify and correct his error.**Question 33**The scatterplot compares the math and science grades of 24 high school students.A. Use the best fit line to predict the science grade of a student with an 88 in math.B. What grade does the best fit line predict for someone with a 68 in math? What is the error in this prediction?**Question 34**Factor the following polynomial 6x6 – 4x5 + 9x – 6**Question 35**Teloria, Maria, and Britt each ordered a pizza. Teloria ate 4/7 of hers, Maria ate .75 of hers, and Britt ate 5 of her 8 slices. Order the girls, from greatest to least, according to how much of their pizzas they ate.**Question 36**There is a bag filled with marbles: 5 red, 8 blue, 4 yellow, and 3 green. You want to draw a red then a blue marble. Do you have a better chance of drawing a red then a blue marble with or without replacing the first marble? Explain your answer.**Question 37**A store is having a sale on 200 DVD movies. Some of the movies are being sold for $10 and some of them are being sold for $12. If the store made $2200 after selling all 200 DVDs, how many $12 DVDs were sold?**Question 38**The boxplots show data gathered from asking 300 buyers of BMWs how old they were at the time of purchase. Answer each question a. Which data set has the largest median? b. Which data set has the largest range? c. Which data set has the largest interquartile range? d. Which data set might contain an outlier? e. Which data set appear most skewed, and how is it skewed?**Question 39**• Jim is less than 4 times younger than Ed, while Ed is a third of the age of Billy. Billy is 96 years old. Determine an inequality for the possible range of values for Jim’s age.**Question 40**List the numbers in order from least to greatest.**Question 41**George picked flowers every day for three days. On the first day George picked 2 flowers. On the second day George picked 6 flowers, and on the third day he picked 10. A function can be written to model George’s sequence. What is the slope of that function?